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Recent gullies on Mars are suspected to be the result of liquid-water-bearing flows. A formation from wet flows has been challenged by studies invoking granular (dry) flows. Our study focuses on the sinuous shapes observed for some of the recent Martian gullies. Sinuous gullies are found in locations and slopes (of 10°–15°) similar to straight gullies, and they are therefore related to the same formation processes. Numerical simulations of granular flows are performed here by introducing topographic variations such as obstacles, roughness, or slope changes that could possibly generate flow sinuosity. None of these simulations was able to reproduce sinuous shapes on a slope lower than 18° with friction angles typical of dry granular material. The only way to simulate sinuous shapes is to create small-amplitude periodic variations of the topography of the deposit, an origin not supported by current Martian imagery. Given the presence of sinuosity in natural terrestrial debris flows, we have concluded that sinuous Martian gullies are better reproduced by liquid-water-bearing debris flows. Sinuous shapes in leveed flows are used to derive mechanical parameters from several Martian gullies using photoclinometry. Values in yield strength of 100–2200 Pa, velocities of 1.1–3.3 m s−1, and viscosities from 40 to 1040 Pa s are found, which are all within the range of values for terrestrial debris flows with various proportions of liquid water (20%–40%).